The wrongdoer may receive part of the justice that is due to him in this world, but it will remain incomplete.
The same is true of someone who deserves great reward and repayment - who has done much good, helped or taught many people, saved lives, suffered to uphold truth or patiently endured much hardship or injustice. No earthly compensation is adequate for such relentless courage and effort. These types of deeds can only be repaid in full in an eternal life where every individual affected by one's actions will testify for or against that person, and where one's innermost thoughts and intentions, known only to Allah, will be exposed and judged precisely and perfectly.
Belief in the Hereafter is completely logical. Allah has made certain things pleasing and desirable to us in this worldly life, such as justice, although it is usually unattainable.

Though a person may obtain a good portion of earthly pleasures and many of his objectives, one remains convinced that the world is unjust. Now, why would the Creator implant in us the love for something we may not experience? The answer is that this life is only one portion of our existence and the Hereafter is the necessary conclusion which balances everything out. Whatever is missing here will be found there; and similarly, whatever is gained unlawfully here will result in deprivation there. That is the perfect and absolute justice Allah has promised.

Finally, Allah is able to create and re-create as He wills. He creates whatever He wills, however He wills, whenever He wills. Allah, the Exalted, says “even as We produced the first creation, so shall We produce a new one: a promise We have undertaken: truly shall We fulfil it.” (Quran 21:104)